MinT - Best Known (61, 61+43, s)-Nets in Base 2

Best Known (61, 61+43, s)-Nets in Base 2

(61, 61+43, 44)-Net over F₂ — Constructive and digital

Digital (61, 104, 44)-net over F₂, using

trace code for nets [i] based on digital (9, 52, 22)-net over F₄, using
- net from sequence [i] based on digital (9, 21)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
    - an explicitly constructive algebraic function field [i]

(61, 61+43, 52)-Net over F₂ — Digital

Digital (61, 104, 52)-net over F₂, using

trace code for nets [i] based on digital (9, 52, 26)-net over F₄, using
- net from sequence [i] based on digital (9, 25)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
    - Drinfeld modules of rank 1 [i]

(61, 61+43, 230)-Net in Base 2 — Upper bound on s

There is no (61, 104, 231)-net in base 2, because

1 times m-reduction [i] would yield (61, 103, 231)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10 493110 908680 776221 934529 833656 > 2¹⁰³ [i]